A paste of baking soda and water and some elbow grease is one way to remove scorch marks from a ceramic stove top. All-natural solutions or special cleaners designed for ceramic surfaces are preferred, and the milder they are, the better.
Baking soda is a common staple in most kitchens and makes a great nonabrasive paste when mixed with water that is gentle enough for ceramic but also strong enough to tackle tough scorch marks. Mix baking soda and water into a thick, grainy paste and work into the burn mark with a cloth using small circular motions. It may take several passes for the scorch to start to fade.
Another household scrubber that is also nonabrasive but slightly more alkaline than baking soda is cream of tartar. It is mixed with water to form a paste and applied the same way as the baking soda, but it tends to dissolve more readily in water, so more cream of tartar will be needed to get the right consistency. Because these methods rely more on elbow grease than chemicals, the burn mark may need to be removed over the course of several sessions. If the burn mark is especially bad, a chemical cleaner specifically designed for use on ceramic may be needed.